Question

Falls resulting in hip fractures are a major cause of injury and even death to the elderly. Typically, the hip’s speed at impact is about 2.0 m/s . If this can be reduced to 1.3 m/s or less, the hip will usually not fracture. One way to do this is by wearing elastic hip pads.

A)If a typical pad is 5.0 cm thick and compresses by 2.2 cm during the impact of a fall, what acceleration (in m/s2 ) does the hip undergo to reduce its speed to 1.3 m/s ?

B)What acceleration (in g 's ) does the hip undergo to reduce its speed to 1.3 m/s ?

C)The acceleration you found in part A may seem like a rather large acceleration, but to fully assess its effects on the hip, calculate how long it lasts.

Answer 1

A). Impact speed, u= 2.0m/s

Final speed needed to not have the fracture, v= 1.3m/s

Compression in the elastic hips pad, S= 2.2cm= 0.022m

Then if "a" is the acceleration then by Using eqautions of motion,

(ANS) (negative sign shows that its the decceleration, i.e speed is decreased)

B). We know that acceleration due to gravity is g= 9.8m/s²

Then Acceleration in terms of "g" will be (ANS)

C). Let the time taken to decrease to that much speed is "t", then again using Equations of Motion,

  (ANS)